1. Field of the Invention
This invention relates to a method of and an apparatus for measuring the flow velocity of fluid by using ultrasonic waves and, more particularly, to a method of and an apparatus for measuring the flow velocity of fluid flowing through piping by mounting ultrasonic transducers on the outer surface of a portion of the piping.
2. Description of Background Information
FIG. 9 shows a conventional example. In this example, ultrasonic waves are emitted from an ultrasonic wave vibration element 51 of ultrasonic transducer 50 in a downstream direction and travel via propagation paths l.sub.1, l.sub.2, l.sub.3, l.sub.4, l.sub.5 and reach an ultrasonic wave vibration element 61 of an ultrasonic transducer 60. The propagation time in this case is represented by t.sub.d.
An ultrasonic wave which is emitted from an ultrasonic vibration element 61 of the ultrasonic transducer 60 travels via propagation paths l.sub.5, l.sub.4, l.sub.3, l.sub.2, .sub.1, and reaches the ultrasonic wave vibration 51 of the ultrasonic transducer 50. The propagation in this case is represented by t.sub.u.
In this case, flow velocity in a piping 3 is determined or searched by the equation: EQU V=(C.sup.2 /2D tan .theta..sub.3).multidot.(t.sub.u -t.sub.d) (F-1)
where D represents the inside diameter of piping 3, .theta..sub.3 the angle of refraction in the fluid, and C the sound velocity of the fluid.
As a result, flow velocity at which the fluid flows through the piping 3 can be obtained relatively easily on the basis of the above equation if the sound velocity in the fluid has been previously determined. At the time, the flow rate at which the fluid flows through piping 3 can also be obtained very easily since the inside diameter of piping 3 is known.
However, the directivity, i.e. spreading in the propagation direction of the ultrasonic wave varies considerably depending on the size of a vibration source (vibration element or a vibrating plane). On the other hand, a value, which an angle of incidence .theta..sub.1 can take, greatly depends on this directivity. More specifically, as the vibration source decreases in size, the directivity of the angle of incidence .theta..sub.1 increases in width. For this reason, in measuring the flow rate by the ultrasonic waves, many errors may be easily included in the measured values depending on the measuring conditions.
In general, an angle of directivity .beta. of a first zero radiation angle indicating the magnitude of this directivity is represented by the following equation: EQU .beta..apprxeq.57 .lambda./b.sub.0 (degree) (F-2)
where b.sub.0 indicates a width of the vibration source and .lambda. a wave length of the ultrasonic wave in a propagation medium.
On the other hand, in the ultrasonic transducers for the most commonly used flowmeters, if the size of a surface being in contact with the piping is b, then b.sub.0 =b cos .theta.(where .theta. is a radiation-propagation angle into the piping as in FIG. 9). In actuality, b.sub.0 .apprxeq.5 .lambda. or 8.lambda. in many cases, and the case of b.sub.0 .apprxeq.10 .lambda. is very rare. For this reason, the angle of directivity .beta..apprxeq.5.7.degree. even when b.sub.0 .apprxeq.10 .lambda.. Accordingly, the ordinary ultrasonic transducer has a spreading angle of .+-.13.degree. or more at all times.
As described above, the conventional ultrasonic transducer has a broad directivity, whereby the spreading of the angle of refraction .theta..sub.3 directly causes errors in flow velocity of the fluid as seen in equation (F-2), thus presenting an intrinsic disadvantage that on the wave receiving side, that in order to properly set the angle of refraction, much time and labor have been required for specifying the central position of the ultrasonic wave being propagated at a proper angle out of beams having broad angle widths.
At the same time, there are many cases where spreading of the angle of directivity of the propagated ultrasonic wave approaches or includes one or two excitation conditions (determined by the angle of incidence) out of a plurality of resonance modes (`a` mode of `s` mode of lamb wave) peculiar to the thickness of piping.
For this reason, on the receiving side, the receiving position is set so as to constantly detect the highest value, whereby other resonance modes high in energy transmittivity are frequently detected, so that considerable errors occur in the detected values. More specifically, the ultrasonic wave beams cannot be regarded as parallel beams because the angle of directivity of the ultrasonic wave is broad, and the propagation path of the ultrasonic wave cannot be accurately specified in all parts of a wedge member, a piping wall and the fluid in the piping because propagation can occur in an unexpected direction due to a harmful mode. Therefore, it becomes difficult to determine how much time has been required for traveling through the fluid in the piping out of both the propagation times t.sub.u and t.sub.d, which have been measured, thus presenting such a disadvantage that in the conventional type ultrasonic flow velocity-flow rate meters, the measuring principle, which is based on the Doppler effect, intrinsically lacks reliable measurement.
The angle of the ultrasonic wave radiated into the fluid by the resonance mode is determined by a phase velocity of the lamb wave propagated in the wall of the piping due to the resonance mode and the sound velocity of the fluid.
Accordingly, for the substantial angle of refraction in the case where the ultrasonic wave in propagated in the fluid and received, there are many cases where an angle of input .theta..sub.1 in the wedge member does not coincide with the angle of refraction .theta..sub.3 determined by Snell's law. For this reason, considerable errors occur in the measured values, thus presenting a lack of reliability.